Computer Science: An Overview Tenth Editionnypgand1/IntroToCS2012/slides/PPT_Chap_05.pdf · An algorithm is an ordered set of unambiguous, executable steps that defines a terminating

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Chapter 5: Algorithms

Computer Science: An Overview Tenth Edition

by

J. Glenn Brookshear

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5-2

Chapter 5: Algorithms

• 5.1 The Concept of an Algorithm • 5.2 Algorithm Representation • 5.3 Algorithm Discovery • 5.4 Iterative Structures • 5.5 Recursive Structures • 5.6 Efficiency and Correctness


Definition of Algorithm

An algorithm is an ordered set of unambiguous, executable steps that defines a terminating process.


Algorithm Representation

• Requires well-defined primitives • A collection of primitives constitutes a

programming language.


Figure 5.2 Folding a bird from a square piece of paper


Figure 5.3 Origami primitives


Pseudocode Primitives

• Assignment name expression

• Conditional selection if condition then action


Pseudocode Primitives (continued)

• Repeated execution while condition do activity

• Procedure procedure name (generic names)


Figure 5.4 The procedure Greetings in pseudocode


Polya’s Problem Solving Steps

• 1. Understand the problem. • 2. Devise a plan for solving the problem. • 3. Carry out the plan. • 4. Evaluate the solution for accuracy and

its potential as a tool for solving other problems.


Getting a Foot in the Door

• Try working the problem backwards • Solve an easier related problem

– Relax some of the problem constraints – Solve pieces of the problem first (bottom up

methodology) • Stepwise refinement: Divide the problem into

smaller problems (top-down methodology)


Ages of Children Problem

• Person A is charged with the task of determining the ages of B’s three children. – B tells A that the product of the children’s ages is 36. – A replies that another clue is required. – B tells A the sum of the children’s ages. – A replies that another clue is needed. – B tells A that the oldest child plays the piano. – A tells B the ages of the three children.

• How old are the three children?


Figure 5.5


Iterative Structures

• Pretest loop: while (condition) do (loop body)

• Posttest loop: repeat (loop body) until(condition)


Figure 5.6 The sequential search algorithm in pseudocode


Figure 5.7 Components of repetitive control


Figure 5.8 The while loop structure


Figure 5.9 The repeat loop structure


Figure 5.10 Sorting the list Fred, Alex, Diana, Byron, and Carol alphabetically


Figure 5.11 The insertion sort algorithm expressed in pseudocode


Recursion

• The execution of a procedure leads to another execution of the procedure.

• Multiple activations of the procedure are formed, all but one of which are waiting for other activations to complete.


Figure 5.12 Applying our strategy to search a list for the entry John


Figure 5.13 A first draft of the binary search technique


Figure 5.14 The binary search algorithm in pseudocode


Figure 5.15: Binary search for Bill


Figure 5.16: Binary search for David


Figure 5.17: Binary Search for David


Algorithm Efficiency

• Measured as number of instructions executed

• Big theta notation: Used to represent efficiency classes – Example: Insertion sort is in Θ(n2)

• Best, worst, and average case analysis


Figure 5.18 Applying the insertion sort in a worst-case situation


Figure 5.19 Graph of the worst-case analysis of the insertion sort algorithm


Figure 5.20 Graph of the worst-case analysis of the binary search algorithm


Software Verification

• Proof of correctness – Assertions

• Preconditions • Loop invariants

• Testing


Chain Separating Problem

• A traveler has a gold chain of seven links. • He must stay at an isolated hotel for seven nights. • The rent each night consists of one link from the

chain. • What is the fewest number of links that must be

cut so that the traveler can pay the hotel one link of the chain each morning without paying for lodging in advance?


Figure 5.21 Separating the chain using only three cuts


Figure 5.22 Solving the problem with only one cut


Figure 5.23 The assertions associated with a typical while structure

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Computer Science: An Overview Tenth Editionnypgand1/IntroToCS2012/slides/PPT_Chap_05.pdf · An algorithm is an ordered set of unambiguous, executable steps that defines a terminating